Breaking of the Lorentz symmetry
superconformal transformations break the Lorentz symmetry 
down to 
.
But 
superconformal transformations preserve the full Lorentz symmetry.To understand the Lorentz symmetry, we define ten superfields 
in the following way:
in the following way:
simply speaking, to define
, we take
and substitute
and
A characteristic property of superconformal transformations (as a subgroup of ) is that
they commute with the standard action of the Lorentz group on .
superconformal transformations (as a subgroup of ) is that
they commute with the standard action of the Lorentz group on .